Distribution of Points and Hardy Type Inequalities in Spaces of Homogeneous Type

摘要

In the setting of spaces of homogeneous type, we study some Hardy type inequalities, which notably appeared in the proofs of local T (b) theorems. We give some sufficient conditions ensuring their validity, related to the geometry and distribution of points in the homogeneous space.We study the relationships between these conditions and give some examples and counterexamples in the complex plane.